This invention relates to video signal processing and is concerned with removing noise from a sequence of images such as a sequence of frames comprising a motion picture.
Many papers discussing noise reduction have been presented during the last two decades or so. Many motion compensated noise reduction methods have also been proposed. The types of noise that we are particularly concerned with are noise such as white Gaussian noise, noise which is equivalent to what one would see on a television if the channel were not tuned properly, and noise such as the graininess one sees when watching an old movie (strictly speaking this graininess is due in part to film grain noise which is not necessarily Gaussian distributed).
Suppose one has a set of images (called herein frames) of an image sequence corrupted by additive Gaussian noise. If the value of a pixel at coordinate (i,j) in frame n of the clean image sequence is I(i,j,n), then the value in the corrupted image g(i,j,n) is EQU g(i,j,n)=I(i,j,n)+.eta.(i,j,n) (1)
where .eta.(i,j,n) is additive white Gaussian noise. By Gaussian distributed noise, one means that if one had a frame containing only noise, and then made a histogram of the pixel values, the histogram would have a Gaussian shape. By white noise one means that the noise value at a particular pixel is uncorrelated with the values at any other pixel in any other frame or in any other part of the same frame. This latter constraint is perhaps the more important one for the following methods to function optimally.
One simple way to reduce the noise in the frames is just to average the frames as they arrive. Therefore a recursive averager can be used as set out below in equation (2), where, I.sub.n (i,j) represents the value of the output pixel which is supposed to be an estimate of the clean image. I.sub.n-1 (i,j) is the previous output image pixel and g.sub.n (i,j) the current noisy image pixel. Therefore the output frame at time k is the average of all the previous k frames. If the frame contains a stationary scene, this would be fine, since the noise would be averaged out. However this is not normally the case and moving objects are blurred by this operation.
A motion compensated averager, such as is disclosed in the article by J. Boyce, `Noise Reduction of Image Sequences Using Adaptive Motion Compensated Frame Averaging` in IEEE ICASSP, Volume 3, pages 461-464, 1992, works much better, as expected. The averaging operation is then directed along motion trajectories and so does not blur motion. However this operation is a purely temporal one and so is sensitive to errors in motion estimation. Furthermore, greater noise attenuation can be obtained by using the spatial information in each frame. An article entitled `Motion-Adaptive Weighted Averaging for Temporal Filtering of Noisy Image Sequences`, by M. Ozkan et al, SPIE Image Processing Algorithms and Techniques III, pages 201-212, February 1992, and that entitled `Motion Compensated Enhancement of Noisy Image Sequences`, IEEE ICASSP, vol.1, pages 2121-2124, 1990, are two papers which introduce spatio-temporal noise reduction tactics that achieve better results than the motion compensated frame averager.
An alternative noise reduction method is disclosed by Ozkan et al in their article entitled `Efficient Multiframe Wiener Restoration of Blurred and Noisy Image Sequences`, IEEE Transactions on Image Processing, Vol. 1, No. 4, pages 453-476, Oct. 1992. This method obtains the Fourier transform of each frame of the sequence to be restored to obtain a sequence of 2D Fourier frequency frames which are processed to reduce noise.